Simplify the following expression: $ r = \dfrac{-1}{10} - \dfrac{-8y}{y + 6} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{y + 6}{y + 6}$ $ \dfrac{-1}{10} \times \dfrac{y + 6}{y + 6} = \dfrac{-y - 6}{10y + 60} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{-8y}{y + 6} \times \dfrac{10}{10} = \dfrac{-80y}{10y + 60} $ Therefore $ r = \dfrac{-y - 6}{10y + 60} - \dfrac{-80y}{10y + 60} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{-y - 6 + 80y }{10y + 60} $ Distribute the negative sign: $r = \dfrac{-y - 6 + 80y}{10y + 60}$ $r = \dfrac{79y - 6}{10y + 60}$